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Question
The ratio in which the x-axis divides the line segment joining the points A (a1, b1) and B (a2, b2) is
Options
b1 : b2
−b1 : b2
a1 : a2
−a1 : a2
Solution
−b1 : b2
Explanation;
Hint:
A line divides internally in the ratio m : n the point P is, `(("m"x_2 + "n"x_1)/("m" + "n"), ("m"_2 +"n"y_1)/("m" + "n"))`
The point P is (a, 0) = `(("ma"_2 + "na"_1)/("m" + "n"), ("mb"_2 + "nb"_1)/("m" "n"))`
∴ `("mb"_2 + "nb"_1)/("m" + "n")` = 0
mb2 + nb1 = 0
⇒ mb2 = −nb1
`"m"/"n" = "b"_1/"b"_2`
∴ m : n = −b1 : b2
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